In addition to the solutions posted previously, you may also want to take a look at MovingAverage. If your x points are equidistant and each xi appears only once, then running MovingAverage[yourlist, n] on your list will give you the average x in the interval (xi, xi+(n-1)*deltax), i=1, ..., and the corresponding average of y in that interval:
data = {
{30, 0.0019},
{31, 0.0024},
{32, 0.0026},
{33, 0.0030},
{34, 0.0034}
};
MovingAverage[data, 3]
{{31, 0.0023}, {32, 0.00266667}, {33, 0.003}}
This produces results in overlapping intervals, which you may or may not want.
Themis